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36^2=36*36 =4*9*4*9 =16*81 =2^4*3^4 =(4+1)(4+1) =25 ( For 16 you can see there are 5 factors and similarly for 81 there are 5 factors) So the ans is the total number of combinations. Is it right suresh?
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The answer choices make this easy: every positive perfect square has an odd number of divisors (because in a perfect square's prime factorization, all of the exponents must be even; when you add one to each and multiply, you will be multiplying only odd numbers, and the product will therefore be odd). So without doing any work, the answer must be 25.
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36^2=36*36 =4*9*4*9 =16*81 =2^4*3^4 =(4+1)(4+1) =25 ( For 16 you can see there are 5 factors and similarly for 81 there are 5 factors) So the ans is the total number of combinations. Is it right suresh?

you are right! buddy.
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Your attitude determines your altitude Smiling wins more friends than frowning

@x2suresh: Can you explain this a little further? I'm not sure I understand how how you did this.

Also, thanks for all your posts on this site. They are very helpful!

In general here is the formula for finding factors

2^n * 3^m

factors for 2^n 2^0, 2^1, 2^2 ... 2^n ---> (n+1) factors for 2^n factors for 3^m 3^0, 3^1, 3^2,....3^m ---->(m+1) factors for 3^m

So No.of factors for 2^n * 3^m = combination of factors for 2^n *3^m = (n+1)(m+1)

Is it clear.

Just want to add that it does not need to be in the form of 2^n 3^m It just needs to be expressed in the form of its prime factors raised to some power.

@x2suresh: Can you explain this a little further? I'm not sure I understand how how you did this.

Also, thanks for all your posts on this site. They are very helpful!

In general here is the formula for finding factors

2^n * 3^m

factors for 2^n 2^0, 2^1, 2^2 ... 2^n ---> (n+1) factors for 2^n factors for 3^m 3^0, 3^1, 3^2,....3^m ---->(m+1) factors for 3^m

So No.of factors for 2^n * 3^m = combination of factors for 2^n *3^m = (n+1)(m+1)

Is it clear.

Just want to add that it does not need to be in the form of 2^n 3^m It just needs to be expressed in the form of its prime factors raised to some power.

thats correct!! It is just an example.
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Your attitude determines your altitude Smiling wins more friends than frowning

I just love these types of questions - high difficulty level, but with a 'shortcut' to solve it in less than a minute. I got this question in the CAT this weekend, couldn't figure out how to solve it and guessed wrong. Saw the explanation after the test and it struck me as beautiful
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